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Math Help - Max Point

  1. #1
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    Max Point

    A) Find the coordinates of the absolute maximum point for the curve
    y=xe^(-kx) where k is a fixed positive number.Justify your answer

    B) Write an equation for the set of absolute maximum points for the curves y=xe^(-kx) as k varies through positive values

    Im not really sure where to start with this. It is a calc ab problem. I think i would start with the derivative which woule be -ke^(-kx)+e^(-kx). After that im not sure where to go
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  2. #2
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    Quote Originally Posted by calc_help123 View Post
    A) Find the coordinates of the absolute maximum point for the curve
    y=xe^(-kx) where k is a fixed positive number.Justify your answer

    B) Write an equation for the set of absolute maximum points for the curves y=xe^(-kx) as k varies through positive values

    Im not really sure where to start with this. It is a calc ab problem. I think i would start with the derivative which woule be -k x e^(-kx)+e^(-kx). Mr F says: No. You're missing the red x.

    After that im not sure where to go
    0 = -k {\color{red}x} e^{-kx} + e^{-kx} \Rightarrow e^{-kx} (1 - kx) = 0 \Rightarrow x = \frac{1}{k}.

    Now you have to test the nature of this solution. Using the second derivative test might be the easiest way.
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  3. #3
    Member OnMyWayToBeAMathProffesor's Avatar
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    so when u plug the \frac{1}{k} back in to the original equation you get \frac{e^{\frac{-x}{k}}}{k} correct? but how would i tackle part b?
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  4. #4
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    Quote Originally Posted by OnMyWayToBeAMathProffesor View Post
    so when u plug the \frac{1}{k} back in to the original equation you get \frac{e^{\frac{-x}{k}}}{k} correct? but how would i tackle part b?
    did you perform the second derivative test as recommended by Mr. F ?
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